The points A (2, 0), B (9, 1), C (11, 6) and D (4, 4) are the vertices of a quadrilateral ABCD. Determine whether ABCD is a rhombus or not.

Question

Philoid · Accepted Answer

Here given points are A (2, 0), B (9, 1), C (11, 6) and D (4, 4).

For a quadrilateral to be rhombus, all sides must be equal.

By distance formula,

XY =

For side AB,

AB =

=

= units.

For BC,

BC =

=

= units

CD =

=

= units.

AD =

=

= units.

Here all sides are unequal.

Hence □ABCD is not a rhombus.